Probabilistic Constraint Satisfaction: Application to Radiosurgery

Abstract: Although quite successful in a variety of settings, standard optimization
approaches can have drawbacks within medical applications. For example,
they often provide a single solution which is difficult to explain, or
which can not be incrementally modified using secondary "soft" constraints
that are difficult to encode within the optimization. In order to address
these issues, we have developed a probabilistic optimization technique that
allows the user to enter prior probability distributions (Gaussian) for the
parameters to be optimized as well as for the constraints on the
parameters. Our technique combines the prior distributions with the
constraints using Bayes' rule. The algorithm produces not only a set of
parameter values, but variances on these values and covariances showing the
correlations between parameters. We have applied this method to the problem
of planning a radiosurgical ablation of brain tumors. The radiation plan
should maximize dose to tumor, minimize dose to surrounding areas, and
provide an even distribution of dosage across the tumor. It also should
be explainable to and modifiable by the expert physicians based on external
considerations. We have compared the results of our method with the
standard linear programming approach.